The voice on the phone is husky, familiar, and just a little menacing. “I was told to call this number,” the speaker says. I give a little shudder before realising it’s Viggo Mortensen, calling as planned to talk about his new film, The Two Faces of January. Phew.

He sounds a little weary, which is fair enough as he’s calling from the back seat of a car that’s taking him from downtown London, where he’s just done a couple of days of promotion, to the airport, to catch a flight to Madrid, which has been his home for the past few years. He likes it there, he says. “As a child I lived in a Spanish-speaking country, Argentina. It’s not exactly the same but there’s a lot of things that are similar. I’m comfortable there.”

An accomplished painter and photographer, Mortensen also speaks Danish – his father is from Denmark – so it is something of a paradox that in The Two Faces of January this multi-talented polyglot should play an American abroad who is out of his depth in all respects.

“It was kind of fun to speak with an atrocious accent,” Mortensen says of his character, Chester MacFarland, a seemingly well-to-do businessman on holiday in 1960s Greece with his wife Colette (Kirsten Dunst). “He’s speaking in a muddle of Greek and Italian; that was sort of a funny little touch.”

Chester is, in fact, a conman, a financial adviser who has swindled his clients out of a fortune; he’s not on holiday, but on the run. Indeed, even as he gets deeper into trouble he remains elusive.

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Playing a character who is so slippery is enormously enjoyable, he says. After all, an actor’s professional life is all about pretending to be someone else. “[As an actor], you lie as well as you can, that’s what you’re paid to do. And in this case I’m lying about a guy who’s lying about being this person who’s lying about being another person. It’s kind of like a hall of mirrors. Instead of looking in one mirror and trying to be that person as an actor, it’s a whole series of mirrors. It’s fun.”

The film is essentially a three-hander, with Oscar Isaac (the Llewyn Davis of the Coen brothers’ recent film) providing the third corner of a slightly bizarre love triangle. He’s a tour guide called Rydal, a man with troubles of his own back home, who agrees to help the MacFarlands out of a tight spot – mostly because he’s fallen for Mrs MacFarland.

It is based on a 1964 novel by Patricia Highsmith, and there are distinct echoes in it of her The Talented Mr Ripley. There’s that sense of 1960s Europe as a cheap playground for wealthy Americans in great clothes. And there’s another portrait of a social climber who thinks nothing of donning an assumed persona to gain entry to the class to which he aspires. Where it differs, though, is in the nature of the character at its heart.

Tom Ripley – played so brilliantly in Anthony Minghella’s 1999 film by Matt Damon – is a psychopath. Chester is simply a bumbling fool, and the other two are not much better.

“There’s a lot of subterfuge and duplicity but the characters don’t always act in their own self-interest, and that’s what’s interesting about them,” says Mortensen. “All of them on some level are not happy with their lot in life, they want more. If they were happy with what they had, they wouldn’t be where they were and with the people that they’re with.

“I think it was Montesquieu who talked about that – that being happy is a fairly straightforward thing; the problem is that people want to be happier than other people, and the problem with wanting to be happier than other people is other people are never as happy as we think they are. So it’s a mess when you start to go down that road” – he chuckles – “and that’s what happens in this movie”.

It’s a nice touch, that dropping in a line from the 18th century French philosopher, because it echoes an aspect of Chester’s character. Mortensen has a BA (Spanish studies, politics) from St Lawrence University in New York. Chester, by contrast, “is a self-taught guy”. “Andin that way of the autodidact, he’s trying to be up on everything so that he can speak in an informed way with his wife.”

For Mortensen, a scene in which Chester’s tenuous grasp on classicism is shown up by Rydal in front of his wife was the key to understanding the character. “Sometimes you read one line of dialogue like that and you think, ‘OK, I can set that up in an earlier scene by seeing him place importance on buying certain books on Greek mythology at the flea market’. You see him reading them, making an effort to be as knowledgeable as he can in that typical crash-course, self-made-man approach – ‘I can learn about this tonight and be able to talk about it in an informed way tomorrow; I don’t have to go to university for four years’.”

He talks about preparing for the role as if Chester were a real-life person whose tics he had to get down. “I did a thorough research of the character, not just what he would look like and how we would sound and so forth, but from the beginning – what kind of life did he have and what kind of person is he,” he says.

The Chester he imagined was a man who had grown up working-class in the Depression, served in the war, and saw the years immediately after it as an opportunity to recreate himself. Rydal is a child of the Beat generation; Chester has more in common with Mad Men’s Don Draper, a man to whom image is all. “Men of that generation, if they had just one jacket, it was rumpled, they’d put it under the mattress, do whatever they had to, comb their hair back with their hand. Presentation was important,” he says.

But, in portraying such a man, what’s going on inside is just as important – even if the audience never sees it. “It’s nice to have a secret as an actor, for myself,” he says. “Even if a part is written very simply I always try to have an interior life because all people have one. I think even the most tranquil nun in a convent has strange thoughts or dark thoughts or thoughts that she might feel she is going to Hell for having.”

The more he talks, the more you get the impression of Viggo Mortensen as the kind of actor who lives and breathes a character for months before a shoot and for every moment of it. Is that accurate?

“You do show up prepared,” he says. “But I certainly don’t ask people to call me ‘Chester’ on set. There are people who do that sort of thing, make a show of it. Everybody works in their own way.”